We compute the equation and nonminimal resolution F of the carpet of type (a,b) where $a \ge b$ over a larger finite prime field, lift the complex to the integers, which is possible since the coefficients are small. Finally we study the nonminimal strands over ZZ by computing the Smith normal form. The resulting data allow us to compute the Betti tables for arbitrary primes.
i1 : a=5,b=5
o1 = (5, 5)
o1 : Sequence
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i2 : elapsedTime T=carpetBettiTable(a,b,3)
-- 0.00267841 seconds elapsed
-- 0.00680585 seconds elapsed
-- 0.0283945 seconds elapsed
-- 0.0121195 seconds elapsed
-- 0.00423141 seconds elapsed
-- 0.257877 seconds elapsed
0 1 2 3 4 5 6 7 8 9
o2 = total: 1 36 160 315 302 302 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 14 . . . .
2: . . . . 14 288 315 160 36 .
3: . . . . . . . . . 1
o2 : BettiTally
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i3 : J=canonicalCarpet(a+b+1,b,Characteristic=>3);
ZZ
o3 : Ideal of --[x ..x , y ..y ]
3 0 5 0 5
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i4 : elapsedTime T'=minimalBetti J
-- 0.163073 seconds elapsed
0 1 2 3 4 5 6 7 8 9
o4 = total: 1 36 160 315 302 302 315 160 36 1
0: 1 . . . . . . . . .
1: . 36 160 315 288 14 . . . .
2: . . . . 14 288 315 160 36 .
3: . . . . . . . . . 1
o4 : BettiTally
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i5 : T-T'
0 1 2 3 4 5 6 7 8 9
o5 = total: . . . . . . . . . .
1: . . . . . . . . . .
2: . . . . . . . . . .
3: . . . . . . . . . .
o5 : BettiTally
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i6 : elapsedTime h=carpetBettiTables(6,6);
-- 0.00573073 seconds elapsed
-- 0.0231988 seconds elapsed
-- 0.150504 seconds elapsed
-- 1.27622 seconds elapsed
-- 0.314682 seconds elapsed
-- 0.0439928 seconds elapsed
-- 0.00748945 seconds elapsed
-- 4.66938 seconds elapsed
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i7 : carpetBettiTable(h,7)
0 1 2 3 4 5 6 7 8 9 10 11
o7 = total: 1 55 320 891 1408 1155 1155 1408 891 320 55 1
0: 1 . . . . . . . . . . .
1: . 55 320 891 1408 1155 . . . . . .
2: . . . . . . 1155 1408 891 320 55 .
3: . . . . . . . . . . . 1
o7 : BettiTally
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i8 : carpetBettiTable(h,5)
0 1 2 3 4 5 6 7 8 9 10 11
o8 = total: 1 55 320 891 1408 1275 1275 1408 891 320 55 1
0: 1 . . . . . . . . . . .
1: . 55 320 891 1408 1155 120 . . . . .
2: . . . . . 120 1155 1408 891 320 55 .
3: . . . . . . . . . . . 1
o8 : BettiTally
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